Geostatistics with different measurement errors

#1
Hello,

I'm having a hard time identifying the subject and possible resources of my problem.

I have spatio-temporal data (Z) coming from environmental sensors that travel around a city. We have the spatial position (x,y), time (t), the variable of interest ( Y here : sound) and potentially other variables related to the environment of the observation (X).

I chose to model the sound as a gaussian process, using geostatistics, more precisely I saw that it was equivalent of making a two level hirarchical model like :

Z/Y ~ N(0 , σ )

Y ~ N( βX, Σ)

Where σ is the mesurment errors of the sensors and Σ the covariance function of the sound process Y.

Now, let's assume that my sensors i ( suppose we have 10) are different (different bias and variance each). I want to model these data as follows :

Z_i/Y ~ N( a_i(t),σ_i) for each sensor i

Y ~ N( βX,Σ)


Where a_i(t) represents a drift in time for sensor i and σ_i the sensor-specific measurement error.

My goal is to estimate all these parameters and to use an estimator like kriging to predict at unsampled locations.

I can't find any resource on the internet about this problem and how to solve it ( data assimilation, geostatistics, hierarchical modling ? )
If you can give me the type of model used to solve this problem or resources that deal with this subject, I will be very grateful.

Sorry if this is vague, feel free to ask me for more info, i appreciate any help.